Magnon-mediated spin transport across nonmagnetic metal (NM) and ferromagnetic insulator (FI) interface depends critically on electron-magnon coupling. We propose a novel route to enhance electron-magnon coupling dynamically from transport viewpoint. Using non-equilibrium Green's function a theoretical formalism for magnon-mediated spin current is developed. In the language of transport, the effective electron-magnon coupling at NM/FI interface is determined by self-energy of FI lead, which is proportional to density of states (DOS) at NM/FI interface due to nonlinear process of electron-magnon conversion. By modifying interfacial DOS, the spin conductance of 2D and 3D NM/FI systems can be increased by almost three orders of magnitude, setting up a new platform of manipulating dynamical electron-magnon coupling.